simplify the expression
![(\sqrt[4]{5 } - \sqrt[3]{2}) (\sqrt[3]{5} + \sqrt[5]{2} )](https://tex.z-dn.net/?f=+%28%5Csqrt%5B4%5D%7B5+%7D++-++%5Csqrt%5B3%5D%7B2%7D%29+++%28%5Csqrt%5B3%5D%7B5%7D++%2B++%5Csqrt%5B5%5D%7B2%7D+%29 "(\sqrt[4]{5 } - \sqrt[3]{2}) (\sqrt[3]{5} + \sqrt[5]{2} )")
Answers
Step-by-step explanation:
Rationalize the denominator: \frac{\sqrt{3}}{\sqrt{7+\sqrt{5}}} \cdot \frac{\sqrt{7+\sqrt{5}}}{\sqrt{7+\sqrt{5}}}=\frac{\sqrt{3}\sqrt{7+\sqrt{5}}}{7+\sqrt{5}}
7+
5
3
⋅
7+
5
7+
5
=
7+
5
3
7+
5
.
\frac{\sqrt{3}\sqrt{7+\sqrt{5}}}{7+\sqrt{5}}
7+
5
3
7+
5
2 Rationalize the denominator: \frac{\sqrt{3}\sqrt{7+\sqrt{5}}}{7+\sqrt{5}} \cdot \frac{7-\sqrt{5}}{7-\sqrt{5}}=\frac{\sqrt{3}\sqrt{7+\sqrt{5}}(7-\sqrt{5})}{{7}^{2}-{\sqrt{5}}^{2}}
7+
5
3
7+
5
⋅
7−
5
7−
5
=
7
2
−
5
2
3
7+
5
(7−
5
)
.
\frac{\sqrt{3}\sqrt{7+\sqrt{5}}(7-\sqrt{5})}{{7}^{2}-{\sqrt{5}}^{2}}
7
2
−
5
2
3
7+
5
(7−
5
)
3 Simplify {7}^{2}7
2
to 4949.
\frac{\sqrt{3}\sqrt{7+\sqrt{5}}(7-\sqrt{5})}{49-{\sqrt{5}}^{2}}
49−
5
2
3
7+
5
(7−
5
)
4 Use this rule: {\sqrt{x}}^{2}=x
x
2
=x.
\frac{\sqrt{3}\sqrt{7+\sqrt{5}}(7-\sqrt{5})}{49-5}
49−5
3
7+
5
(7−
5
)
5 Simplify 49-549−5 to 4444.
\frac{\sqrt{3}\sqrt{7+\sqrt{5}}(7-\sqrt{5})}{44}
44
3
7+
5
(7−
5
)
Answer:
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